Question: Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-2x-5y &= 1 \\ 4x+4y &= 8\end{align*}$
Begin by moving the $y$ -term in the second equation to the right side of the equation. $4x = -4y+8$ Divide both sides by $4$ to isolate $x$ $x = {-y + 2}$ Substitute this expression for $x$ in the first equation. $-2({-y + 2}) - 5y = 1$ $2y - 4 - 5y = 1$ Simplify by combining terms, then solve for $y$ $-3y - 4 = 1$ $-3y = 5$ $y = -\dfrac{5}{3}$ Substitute $-\dfrac{5}{3}$ for $y$ in the top equation. $-2x-5( -\dfrac{5}{3}) = 1$ $-2x+\dfrac{25}{3} = 1$ $-2x = -\dfrac{22}{3}$ $x = \dfrac{11}{3}$ The solution is $\enspace x = \dfrac{11}{3}, \enspace y = -\dfrac{5}{3}$.